We present an investigation into the use of an explicitly correlated plane wave basis for periodic wavefunction expansions at the level of second-order Møller-Plesset (MP2) perturbation theory. The convergence of the electronic correlation energy with respect to the one-electron basis set is investigated and compared to conventional MP2 theory in a finite homogeneous electron gas model. In addition to the widely used Slater-type geminal correlation factor, we also derive and investigate a novel correlation factor that we term Yukawa-Coulomb. The Yukawa-Coulomb correlation factor is motivated by analytic results for two electrons in a box and allows for a further improved convergence of the correlation energies with respect to the employed basis set. We find the combination of the infinitely delocalized plane waves and local short-ranged geminals provides a complementary, and rapidly convergent basis for the description of periodic wavefunctions. We hope that this approach will expand the scope of discrete wavefunction expansions in periodic systems.
Explicitly correlated plane waves: Accelerating convergence in periodic wavefunction expansions
Andreas Grüneis, James J. Shepherd, Ali Alavi, David P. Tew, George H. Booth; Explicitly correlated plane waves: Accelerating convergence in periodic wavefunction expansions. J. Chem. Phys. 28 August 2013; 139 (8): 084112. https://doi.org/10.1063/1.4818753
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